Gas analyzer



Aug. 8, 1 967 J. w. THOMAS 3,334,513

GAS ANALYZER Filed May 15, 1964 3: 2 30) 10 J6 n 1 1,: VACUUM l PUMPnurse nuwomm PUMP 7 I SAM/1L1 j] 29) 38 \/.'M. I @ael STANDARD v.,M. I(e.9.AlR) l VACUUM PUMP FILTER HUMtmF'lER PUMP -I-= I .9 I J co manna:TEMPERATURE ucnosFnTZf Eh-5 Patented Aug. 8, 1967 3,334,513 GAS ANALYZERJess W. Thomas, Chatham, N.J., assignor to Whirlpool Corporation, acorporation of Delaware Filed May 15, 1964, Ser. No. 367,645 8 Claims.(Cl. 73-23) This invention relates to a continuous gas analyzer in whichthe amount of a third gas in a mixture with a pair of other gases isindicated substantially regardless of the amount of either of the pairof other gases.

A continuous analyzer for the amount of one gas of a mixture of the onegas with another gas by indicating flow characteristics is old in theart. However, with this invention it is now possible to indicate theamount, and particularly the varying amount, of a third gas mixed with apair of other gases substantially without regard to the amount of eitherof the pair of other gases.

One of the features of this invention therefore is to provide animproved apparatus for indicating the amount, and particularly thevarying amount, of a third gas in a mixture with two other gases.

Another feature of the invention is the provision of such an apparatuswhich is extremely inexpensive and simple in structure yet whichprovides accurate indication of the amount of the gas being analyzed.

Other features of the invention will be apparent from the followingdescription of certain embodiments thereof as shown in the accompanyingdrawing.

The single figure of the drawing is a diagrammatic View of one systemfor indicating the amount of a third gas' in a mixture with a pair ofgases without regard to the varying amounts of either of the pair ofgases so long as the first gas of the pair has a lower molecular weightand a higher viscosity than the molecular weight and viscosity of thesecond gas of the pair.

The gas analyzer of this invention operates by indicating the varyingresistance to flow of a mixture of at least three gases as the directresult of varying amounts of one of these gases and substantiallyregardless of varying amounts of the other two, with this varyingresistance being utilized to indicate precisely the varying amounts ofthe one gas.

In the embodiment of the drawing there is provided a system 30 having afirst line 10 for a mixture of gases. This mixture comprises a pair ofgases mixed with a third gas in which a first gas of the pair has alower molecular weight and higher viscosity than the molecular weightand viscosity of the second gas of the pair. In this embodiment the line10 includes a vacuum pump 11 for drawing in a sample of mixed gases tobe analyzed through an inlet line 12 and a filter 13 for filtering outfrom the gases foreign materials such as solids. In the line 10 there isalso located a humidifier 29 for saturating the mixed gases withmoisture vapor. The gases are saturated in order to eliminate the effectthat varying moisture content of the incoming gas mixture would have onthe observed results.

From the humidifier the line continues to a capillary 14 havingparticular dimensions as explained later. Downstream of the capillary 14is a positive displacement pump 15 which draws a constant flow of gasthrough the capillary. As shown, the line 10 also includes a bleed-offline 16 of the ordinary type. The combination of the vacuum pump 11 fordrawing the sample to be analyzed into the line and the bleed-off line16 functions to supply the gas to be analyzed to the entrance 17 of thecapillary at substantially atmospheric pressure. Thus, the vacuum pump11 draws in the gas sample to be analyzed at a pressure that is slightlyin excess of atmospheric and the bleed-off line 16 eliminates theexcess.

In system 30, the test capillary 14 is supplied with the gas mixture atatmospheric pressure and the volume drawn through the capillary ismaintained constant by the positive displacement pump 15. Variations inconsistency of the gas being tested are therefore indicated by thepressure drop through the capillary 14.

If desired, the vacuum pump 11, filter 13 and humidifier 29 can beeliminated, particularly if the gas sample being tested is substantiallyfree of foreign material and if the highest degree of accuracy is notrequired. The varying characteristics of the gas mixture being testedare indicated by the pressure drop through the capillary as shown by apressure gauge 18.

The vacuum pump 11, filter 13 and humidifier 29 are employed as shownand in addition there is an identical counterbalancing second line 19arranged in parallel with the first line 10 and also containing a vacuumpump 20, filter 21, humidifier 22 and positive displacement pump 23,each as nearly as possible identical with the cone sponding element inthe first line 10. The second line 19 is adapted to draw in, through aninlet line 24, a standard gas that is substantially unvarying inconsistency, e.g., the standard gas may be air.

In order to indicate the varying characteristics of the gas mixturebeing tested, the pressure gauge 18 is connected across the lines 10 and19 downstream from the capillaries 14 and 25. As the standard gas in thesecond line 19 is unvarying, changes in the gauge 18 will indicatechanging characteristics of the gas sample being tested. Any changingexterior environmental factors will affect both the test gas and thecounterbalancing gas alike.

In the second line 19 there is also provided zero control valve 26 inorder to permit accurate zeroing of the analyzer. This is necessarybecause the capillaries 14 and 25 cannot be made exactly identical. Inorder to correct for this, identical gases are drawn through the twolines 10 and 19 and the measuring capillary 14 and counterbalancingcapillary 25, and the valve 26 is adjusted until the pressure indicator18 indicates zero. This adjustment compensates for any variations in thetwo capillaries 14 and 25.

Because a standard gas, such as air, is passed through thecounterbalancing capillary 25, the pressure drop therein in passingthrough this capillary is constant. However, the pressure drop throughthe capillary 14 will vary with variations in the constituents of thegas being tested. In order to maintain a uniform and similar temperatureof the gases, the capillaries 14 and 25, as well as the pumps 15 and 23,are placed in a constant-temperature enclosure 27, and the capillariesare placed as close together as possible. This temperature is preferablyhigher than ambient in order to insure against condensation of moisturein the analyzer and particularly in the capillaries.

In the following description of the mathematical basis of thisinvention, the identification of the symbols is given at the end of thisspecification.

The formula for determining the length of the capillary 14 (and thus ofthe identical capillary 25) is as follows:

This formula is effective for a blend of a pair of gases in which afirst gas of the pair has a lower molecular weight. and higher viscositythan the second gas of the pair. The formula is effective for measuringthe length of the capillary regardless of its diameter so long as thediameter is such as to give a pressure drop between the two ends of thecapillary when subjected to fluid flow therein, and so long as theformula gives a positive result. This formula shows that the length ofthe capillary is directly proportional to the gas pressure of the pairof gases at the inlet of the capillary and the volumetric flow rate ofthe gases and the difference in the molecular weights of the two gases.The length is inversely proportional to the absolute temperature anddifference in viscosity of the two gases.

With a capillary of a length determined according to this formula, themixture of the two gases flowed through the capillary gives the samepressure drop regardless of the relative proportions of the two gases.Therefore, any changes in pressure drop in the mixture of the pair ofgases and the third gas whose amount is to be indicated will only becaused by changes in amounts of the third gas in the mixture. This is soaccurate that the gauge 18 may be calibrated to show with a high degreeof accuracy the actual percentages of the third gas in the mixture.

Flow through the capillary 14 is of course a pressurevolumerelationship. The volume is kept constant by the positive displacementump 15 and the apparatus indicates variations in pressure drop throughthe capillary to indicate variations in amount of the third gas. Ifdesired, the relative amounts of the third gas could be indicated bymaintaining the pressure in the line downstream from the capillary 14constant as by the pressure regulator 35 (indicated in phantom) andnoting variations in volume at the pump required to maintain thisconstant pressure as by the volume meter 36 (also indicated in phantom).In the counterbalancing second line 19 there are provided a similarpressure regulator 37 and similar volume meter 38. Therefore, in thesystem of this invention the amount, and particularly variations inamount, of the third gas in the three gas mixture is indicated bymaintaining either the pressure or the volume in the system constant andobserving variations in either the pressure or the volume.

Pressure drop through a capillary such as capillary 14 depends primarilyupon two effects. One of these is the pressure drop in the body of thecapillary between the two ends 17 and 28 which is due to the viscosityof the gases flowing through the capillary. The other pressure dropcause is the effect of the entrance end 17 and exit end 28 of thecapillary as these ends operate as orifices. The pressure drop due tothese orifice effects is a function of the molecular weight of thefluids. The mathematical expression of this pressure drop through thecapillary is 7T7 Mw 1r r Mw (2) where P is pressure at the entrance end17 to the capillary and P is the pressure at the exit end 28.

The above equation is a preferred form of the Brillouin equation (M.Brillouin, Lecons sur la Viscosit des Liquids et des Gas, vol. 1, p.133; vol. 2, p. 37). In Equation 2 the first portion to the right of thesecond equal sign is an expression of the pressure drop in the body ofthe capillary which is a function of the viscosity of the fluids whilethe last portion of the equation is an expression of pressure drop dueto the orifice effects and is related to the molecular weight asexplained above. As indicated, these are additive to give the totalpressure drop (AP) through the capillary.

This Equation 2 of Brillouin is based on Poiseuilles law (Partington, I.R., An Advanced Treatise on Physical Chemistry, 1st ed., p. 881,Longmans, London, 1949) which may be expressed as follows:

V 7I'(P1P2)T t 81113 in which V is measured at mean pressure of /2 (PH-PThis law expresses the gas flow through a capillary tube and assumes noslip, i.e., that the fluid velocity at the tube wall is Zero.

Equation 2 is the same as Equation 3 except Equation 2 is corrected forend effects. At very low pressures slip becomes important. However, theslip can be ignored when the fluids flowing through the capillaries areat a pressure that is near atmospheric, as any error due to the slipeffect is extremely small.

4 As reported by Benton (A. F. Benton, Phys. Rev. 14, pp. 403-408,1919), Brillouins formula for expressing fluid flow through a capillaryincluding end effect conditions is in which P and d are measured underthe same conditions. For the purpose of this invention, however, thisFormula 4 is expressed in Formula 2 wherein the term P/d has beenreplaced by the equivalent RT /M w, since In order for these formulas towork and thus in order to design the apparatus of this invention, it isnecessary that the fluids flowing through the capillary be in streamlineflow. This, of course, requires that the Reynolds number must not begreater than 2100.

As explained above, Equation 1 gives the length of the capillary for thepair of fluids regardless of the relative amounts of each fluid in theblend of the pair of fluids. With this calculated length, the pressuredrop for both fluids of the pair of fluids through the capillary will besubstantially identical so that the blend of the pair of fluids operatesas a single fluid. This is proven as follows.

The Brillouin Equation 2 Written to equate the pressure drops of fluids1 and 2 of the pair of fluids is as follows:

The subscripts l and 2 are used to identify the first fluid (having thelower molecular weight and greater viscosity of the pair) and the secondfluid, respectively, of the pair of fluids.

The mass flow rates M and M are related as follows when the preferredpositive displacement pump is used:

M1 PioP- R PZQP- (7) where Q is measured at the pressure P.

As the pressure drops are equal, P equals P so that the mass flow ratesare related as follows:

This Equation 9 expresses the conditions that must exist for the pair offluids to have the same pressure drop through the capillary. As can beseen, Equation 9 is the same as Equation 1.

Because the first and second fluids constituting the pair of fluids hasthe pressure drop effect of a single fluid regardless of the relativeamounts of each of the pair of fluids the introduction of a third fluidwill mean that this resulting mixture will have pressure drop variationsdue to the varying amounts of the third fluid only.

In order for the pair of fluids to act as a single component in thepressure drop through the capillary, it is necessary, as mentionedabove, that Equation 1 give a positive value which means that the firstfluid of the pair of fluids must have a lower molecular weight and ahigher viscosity than the molecular weight and viscosity of the secondfluid.

Typical pairs of gases which act as a single gas in passing through thecapillary are the following two-component mixtures of gases:

The continuous gas analyzer of this invention is parpreservation ofplant and animal materials as disclosed in Bedrosian and Brody US.Patent No. 3,102,777, issued Sept. 3, 1963, and assigned to the sameassignee as the present application.

Here the system as described above and as illustrated in the drawing isvery useful for continuously indicating the amount of oxygen in themixture of oxygen, carbon dioxide and nitrogen of the inert gases. Theother inert gases in air are present in such minor amounts that they maybe ignored.

Nitrogen has a lower molecular weight and a higher viscosity than hascarbon dioxide. Thus, When passed through a capillary of a lengthdetermined by the above Formula 1 and any diameter (preferably at least0.2 mm.) so long as streamline flow exists, the carbon dioxide andnitrogen will give the same pressure drop as if only a single gas werepresent and without regard to any variations in the amounts of carbondioxide and nitrogen.

Thus, any variations in the pressure-volume relationship will be duesolely to the varying amounts of oxygen. Where the volume is keptconstant these variations will be indicated by variations in pressureand these can be calibrated easily to show the percentage of oxygen inthe mixture. Similarly, when the pressure is kept constant variations inthe amount of oxygen will result in varia tions in the volume passingthrough the capillary and here again this can be calibrated to showpercentages of oxygen.

To prove that any mixture of fluids 1 and2 will have the same pressuredrop as all fluid l or all fluid 2, with fluids 1 and 2 defined asabove, let x be the mol fraction of fluid 2, and (1-x) be the molfraction of fluid 1, and Mw and 1 be the molecular Weights andviscosities of the resulting mixture. Then Mw =Mw x+Mw (l-x) (10) and toa good approximation The conditions for the same pressure drop for themixture as for fluid l or 2 is that L be the same with Mw, and 1substituted for Mw and 1 in Equation 9, or, does and Equation 12 isproven. This means: that the mixture requires the same length L to givethe same pressure drop as fluid 1 or fluid 2.

In one embodiment of the invention, the suction at each of pumps 15 and23 with nitrogen flowing through each capillary 14 and 25, each having adiameter of 0.061 cm., Was 11.0 inches of Water giving P =0.7 l0dynes/cm. Pump displacement Q was 436 cm. /min. or 7.3 cmfi/sec. Thetemperature was about 25 C. and RT=2.475 10 Theoretical length for no APresponse regardless of proportion of nitrogen and carbon dioxide was,for Equation 9,

L P QP L: 0.90 10 5.77+10 =52 cm.

In the above embodiment of the invention where the amounts of oxygen ina saturated atmosphere of oxygen, carbon dioxide and nitrogen in line 10were measured,

7 and air was used in line 19, the amounts of oxygen varied directlywith the pressure drop through the capillary as shown in the followingtable:

Oxygen Nitrogen Carbon P Gauge Dioxide (inches water) As can be seen,the reading on the gauge changes substantially uniformly with changes inoxygen content and is not affected materially b variations in either thenitrogen or carbon dioxide content.

Symbols Having described my invention as related to the embodiments setout herein, it is my intention that the invention be not limited by anyof the details of description, unless otherwise specified, but rather beconstrued broadly within its spirit and scope as set out in theaccompanying claims.

The embodiments of the invention in which an exclusive property orprivilege is claimed are defined as follows:

1. Apparatus for indicating varying pressure-volume changes in a mixtureof a third gas with a pair of gases with said changes being due tovariations in amounts of said third gas only in which a first gas ofsaid pair has a lower molecular weight and higher viscosity than themolecular weight and viscosity of the second gas of said pair,comprising: means providing a gas line for said mixture; pump means forforcefully flowing said mixture through said line; a capillary tube flowrestrictor forming a part of said line and providing streamline flow ofsaid mixture in said tube, said tube having an entrance and an exit anda length such that said pair of first and second gases has substantiallyconstant pressure-volume flow characteristics in said tube at uniformvolumetric flow rates regardless of the relative proportions of saidpair of gases, the length being determined by the following equation:

M1D2-MUI1 wherein:

L=capillary length, centimeters P=gas pressure of said pair at saidcapillary outlet,

dynes Q =volumetric displacement of pump, cm. per sec. Mw =molecularweight of said first gas Mw =molecular weight of said second gas 1=viscosity of said first gas, poises 1 =viscosity of said second gas,poises R=gas constant, 8314x10 for c.g.s. units T K.;

means for flowing said mixture through said line including saidcapillary; means for maintaining one of said pressure and volume of saidmixture flowing through said capillary constant; and means forsimultaneously measuring variations in the other of said pressure andvolume to indicate said variations in amount of said third gas.

2. The apparatus of claim 1 wherein said means for flowing produces gasflow at substantially constant volume but varying pressure due to saidthird gas, and said indicating means responds to said varying pressure.

3. The apparatus of claim 1 wherein said means for flowing produces gasflow at substantially constant pressure but varying volume due to saidthird gas, and said indicating means responds to said varying volume.

4. The apparatus of claim 1 wherein means are provided for subjectingsaid capillary to substantially constant temperature.

5. Apparatus for indicating varying pressure-volume changes in a mixtureof a third gas with a pair of gases with said changes being due tovariations in amounts of said third gas only in which a first gas ofsaid pair has a lower molecular weight and higher viscosity than themolecular weight and viscosity of the second gas of said pair,comprising: means providing a pair of gas lines; a capillary tuberestrictor forming a part of each said line and providing streamlineflow of said mixture in said tube, said tube having an entrance and anexit and a length such that said pair of first and second gases hassubstantially constant pressure-volume flow characteristics in said tubeat uniform volumetric flow rates regardless of the relative proportionsof said pair of gases, the length being determined by the followingequation:

L P Qp M LUZ-M 10; 8112 1 71 -712 wherein:

L=capillary length, centimeters P=gas pressure of said pair at saidcapillary outlet,

dynes Q =volumetric displacement of pump, cm. per sec.

Mw =molecular weight of said first gas Mw =molecular weight of saidsecond gas v =viscosity of said first gas, poises vg viscosity of saidsecond gas, poises Rzgas constant, 8.3l4 10 for c.g.s. units T= K.; pumpmeans for flowing said mixture through one of said lines including saidcapillary; pump means for flowing a constant component gas through saidother line; means for maintaining in each line one of the volume andpressure therein constant; and means for indicating differences betweenthe two lines in the other of volume and pressure to indicate variationsin amounts of said third gas.

6. The apparatus of claim 5 wherein said means for maintaining maintainsthe volume constant.

7. The apparatus of claim 5 wherein said means for maintaining maintainsthe pressure constant.

8. The apparatus of claim 5 wherein means are provided for subjectingsaid capillaries to substantially constant temperature.

References Cited UNITED STATES PATENTS 1,633,352 6/1927 Tate 73-231,884,896 10/1932 Smith 7323 2,674,118 4/1954 Westmoreland 7355 X3,005,552 10/1961 Muller 73-55 X 3,086,386 4/1963 Kapff 7323 3,234,7812/1966 Bragg 7355 JAMES J. GILL, Acting Primary Examiner.

RICHARD C. QUEISSER, Examiner.

J. F. FISHER, Assistant Examiner.

1. APPARATUS FOR INDICATING VARYING PRESSURE-VOLUME CHANGES IN A MIXTUREOF A THIRD GAS WITH A PAIR OF GASES WITH SAID CHANGES BEING DUE TOVARIATIONS IN AMOUNTS OF SAID THIRD GAS ONLY IN WHICH A FIRST GAS OFSAID PAIR HAS A LOWER MOLECULAR WEIGHT AND HIGHER VISCOSTIY THAN THEMOLECULAR WEIGHT AND VISCOSITY OF THE SECOND GAS OF SAID PAIR,COMPRISING: MEANS PROVIDING A GAS LINE FOR SAID MIXTURE; PUMP MEANS FORFORCEFULLY FLOWING SAID MIXTURE THROUGH SAID LINE; A CAPILLARY TUBE FLOWRESTRICTOR FORMING A PART OF SAID LINE AND PROVIDING STREAMLINE FLOW OFSAID MIXTURE IN SAID TUBE, SAID TUBE HAVING AN ENTRANCE AND AN EXIT ANDA LENGTH SUCH THAT SAID PAIR OF FIRST AND SECOND GASES HAS SUBSTANTIALLYCONSTANT PRESSURE-VOLUME FLOW CHARACTERISTICS IN SAID TUBE AT UNIFORMVOLUMETRIC FLOW RATES REGARDLESS OF THE RELATIVE PROPORTIONS OF SAIDPAIR OF GASES, THE LENGTH BEING DETERMINED BY THE FOLLOWING EQUATION: